# Find the nonzero value of k for which the roots of the quadratic equation 9x2 – 3kx + k = 0 are real and equal.

Given equation is 9x2 – 3kx + k = 0

Comparing with standard quadratic equation ax2 + bx + c = 0

a = 9 b = – 3k c = k

Given that the roots of equation are real and equal

Thus D = 0

Discriminant D = b2 – 4ac = 0

(– 3k)2 – 4.9.k = 0

9 k2 – 36k = 0

9k(k – 4) = 0

9k = 0 or(k – 4) = 0

k = 0 or k = 4

But given k is non zero hence k = 4 for which roots of the quadratic equation are real and equal.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Knowing the Nature of Roots44 mins
Take a Dip Into Quadratic graphs32 mins
Foundation | Practice Important Questions for Foundation54 mins
Nature of Roots of Quadratic Equations51 mins
Getting Familiar with Nature of Roots of Quadratic Equations51 mins
Quadratic Equation: Previous Year NTSE Questions32 mins
Champ Quiz | Quadratic Equation33 mins
Balance the Chemical Equations49 mins
Understand The Concept of Quadratic Equation45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses